Example 5
Two circles intersect at two points A and B. AD and AC are diameters to the two circles (see fig.). Prove that B lies on the line segment DC.
Given: Let two circles be C1 & C2.
AD is the diameter of circle C1
& AC is the diameter of circle C2
To prove: B lies on CD.
Construction: Join AB
Proof
Now,
ABD + ABC = 90 + 90 = 180
Since the sum of angles is 180 ,
they form a linear pair.
Linear pair can only happen on a line.
Therefore, DBC is a line.
B lies on the line segment DC.
Hence proved